In a typical optical imaging system, the scene or object to be imaged is located in front of the optical elements comprising the system; and the image is formed on a focal surface (typically a planar surface) located to the rear of the optical elements comprising the system. However, in some so-called "fish-eye" lens systems, a portion of the scene to be imaged can be located to the rear of the optical elements that comprise the system. Such a "fish-eye" lens system can be said to "look behind" the optical elements that comprise the system--i.e., the optical elements of the system can accept radiation from angles greater than a complete hemisphere.
For an imaging lens system to preserve true perspective, the image size must be proportional to the tangent of the field angle. Consequently, to preserve true perspective for a semi-field angle greater than 90.degree., the image size would be infinite. However, in many imaging applications requiring a wide field angle, a certain amount of image distortion is appropriate in order to accommodate an image plane of reasonable size. In practice, a condition in which the image size is proportional to the field angle itself (rather than to the tangent of the field angle) is deemed to provide an acceptable angular representation of the image--i.e., to substantially preserve angular perspective. This condition is called the f-.theta. condition, and is deemed to preserve an acceptable approximation of true perspective.
Until the present invention, design forms had not been developed for "fish-eye" lens systems capable of accepting infrared radiation from hyper-hemispherical fields of view (i.e., from field angles approaching 270.degree., which is three-quarters of a complete sphere surrounding the entrance aperture) at wide relative apertures (i.e., greater than about f/2) to form images that substantially meet the f-.theta. condition.